Question

Represent the given velocity 230 km/h in the direction 200 degrees

Answer 1

Task. Represent the given velocity $v = 230 \, \mathrm{km/h}$ in the direction $\alpha = 200$ degrees. Solution. The vector $v$ is shown in the following figure:

We should find coordinates $(v_{x}, v_{y})$ of its end. By definition

$$v _ {x} = v \cos \alpha , \qquad v _ {y} = v \sin \alpha .$$

Substituting values we get

$$v _ {x} = v \cos \alpha = 2 3 0 * \cos 2 0 0 {}^ {\circ} = 2 3 0 * (- 0. 9 3 9 6 9) = - 2 1 6. 1 3 k m / h,$$ $$v _ {y} = v \sin \alpha = 2 3 0 * \sin 2 0 0 {}^ {\circ} = 2 3 0 * (- 0. 3 4 2 0 2) = - 7 8. 6 6 5 k m / h.$$

Thus $v = (-216.13, -78.665)$ .